WASHINGTON (AP) -- Nearly six in 10 Americans want stricter gun laws in the aftermath of last month's deadly school shooting in Connecticut, with majorities favoring a nationwide ban on military-style, rapid-fire weapons and limits on gun violence depicted in video games, movies and TV shows, according to a new Associated Press-GfK poll.

A lopsided 84 percent of adults would like to see the establishment of a federal standard for background checks for people buying guns at gun shows, the poll showed.

Three-quarters of Americans said they reacted to the Connecticut massacre with deep anger, while 54 percent said they felt deeply ashamed it could happen in the United States.

President Barack Obama was set Wednesday to unveil a wide-ranging package of steps for reducing gun violence, expected to include a proposed ban on assault weapons, limits on the capacity of ammunition magazines and universal background checks for gun sales.

Many of the more restrictive proposals under consideration, such as the assault-weapons ban, would face stiff congressional opposition, particularly among Republicans.

By contrast, the general public appears receptive to stronger federal action following the

Dec. 14 shooting spree at Sandy Hook Elementary School in Newtown, Conn., which claimed the lives of 20 children and six adults.

Some 58 percent favor strengthening gun laws in the United States. Just 5 percent felt such laws should be loosened, while 35 percent said they should be left unchanged.

In comparison, after the Virginia Tech shootings in 2007, an Associated Press-Ipsos poll found that 47 percent wanted stricter gun laws, 38 percent thought they should remain as is and 11 percent wanted to see them loosened.

Caroline Konczey, 63, a retired Navy officer from Indio, Calif., is among those supporting a ban on military-style assault weapons. "I can't imagine why anyone would want one," she said. "What do you do with that, unless you're a collector?"

She suggested an underlying source of gun violence was the breakdown of the nuclear family and a lack of access to mental health care. "Until you strengthen the structure of the family that teaches respect for people, then this stuff goes down," she said.

Specifically, majorities in the new poll favored a nationwide ban on military-style, rapid-fire guns (55 percent) and limits on the amount and type of gun violence that can be portrayed in video games, movies or on television (54 percent). About half (51 percent) of those surveyed back a ban on the sale of magazines holding 10 or more bullets.

At the same time 51 percent said that they believed laws limiting gun ownership infringe on the public's Second Amendment right to possess and carry firearms. Among Republicans, 75 percent cited such infringement.

There is also a gender gap. Gun control is a more important issue for women, with 68 percent saying it was very or extremely important to them, than for men (57 percent). And women are more likely to back stricter gun laws: 67 percent favor them, compared with 49 percent of men.

"Military-style weapons should be military guns, not John Q. Public guns," said Ellen Huffman, 55, of Huntersville, N.C., who supports a ban on assault-style weapons and high-capacity magazines.

Huffman said early detection of mental health problems would go a long way to curbing gun violence. If such problems are caught early enough "you won't have people killing people," she said.

Among gun owners, just 40 percent back a ban on the sale of military-type, rapid-fire guns, and 37 percent favor a ban on high-capacity magazines, while 66 percent of non-gun owners would ban military-style weapons and 60 percent would ban high-capacity magazines.

However, 80 percent of gun owners do support federal standards for gun-show background checks, as do 87 percent of non-gun owners.

Gun owners lean more Republican than the overall public. Fifty-five percent of them are Republicans, compared with 30 percent who are Democrats.

Overall, 3 in 10 said the shootings caused them to wonder whether you could really be safe anywhere these days, up slightly from 25 percent after Virginia Tech, with parents more apt to react with deep worries about safety issues than non-parents.

And residents of the Northeast were much more likely than those in other regions to say the events in Newtown made them feel strongly that there may be too many guns in this country - 46 percent, vs. 35 percent reacting that way in the South, 30 percent in the West and 28 percent in the Midwest.

Max Lude, 70, a retired teacher from West Frankfort, Ill., said limiting magazines to 10 rounds "is probably the smartest thing they can do" to reduce mass tragedies. Mandatory background checks also would help, as would mandatory prison sentences for those convicted of gun grimes, said Lude, a National Rifle Association member and hunter-safety instructor.

"It's a complicated problem with a complicated solution," he said. "It's not just a one-time, quick-fix deal."

The gun control debate heated up after Adam Lanza, 20, shot his way into the Newtown school on Dec. 14 and killed 26 people before committing suicide. Lanza also killed his mother at her home before the shooting spree. His mother kept guns at the home she shared with her son.

The poll of 1,004 adults was conducted by telephone Jan. 10-14, 2013. It has a margin of error of plus or minus 4 percentage points.